Multiply the following complex numbers: $({-3+4i}) \cdot ({-4i})$
Answer: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-3+4i}) \cdot ({-4i}) = $ $ ({-3} \cdot {0}) + ({-3} \cdot {-4}i) + ({4}i \cdot {0}) + ({4}i \cdot {-4}i) $ Then simplify the terms: $ (0) + (12i) + (0i) + (-16 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 0 + (12 + 0)i - 16i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 0 + (12 + 0)i - (-16) $ The result is simplified: $ (0 + 16) + (12i) = 16+12i $